In this paper we obtain a multivariable commutator lifting inequality,
which extends to several variables a recent result of Foiaş, Frazho, and Kaashoek.
This inequality yields a
multivariable lifting theorem that generalizes the noncommutative commutant
lifting theorem.
This is then used to solve new operator-valued interpolation
problems of
Schur–Carathéodory, Nevanlinna–Pick, and Sarason type on Fock spaces.
Some consequences to norm constrained analytic interpolation in the unit
ball of Cn are also considered.
